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Feb 27, 2013 4:30pm PST
longer. and then it changes into this pentagon-type shape, five-sided object, into this hexagon. and now of course this hexagon has gone back to a pentagon, or a pentagon-type object, five-sided, then to this quadrilateral that we see, finally going down to this triangle and a point. so it's a lot like the sphere case. >> greg, what i like so much about this discussion is that it's actually part of things that happen in the real world all the time. for example, when people are trying to image your body, they actually do it by constructing slices of you using some kind -- you know, like x-rays or whatever it is, and they rebuild your body from those slices. and the other way in which it's come up is in cubist art, in fact. and picasso's idea when he was creating this was actually inspired by discussions of how to see four-dimensional things as three-dimensional slices, which is how we're actually going to try to see four dimensions, like the flatlanders try to see three. >> absolutely. so it's easy to see how art and this would interact in the sense that your understanding here is very mu
Feb 13, 2013 4:30pm PST
different kinds of tilings that involve other kinds of shapes. when you have a pentagon, for example, and you try to imagine tiling it so that it goes to infinity, in effect, you find that you get gaps between the pentagons. you can't tile them evenly on a flat surface, so you have to put it on this kind of surface here. and you can show it in a picture by distorting the shape, by making them smaller as you go further and further out. and so, in principle, these will get really, really tiny as you get further and further out. and you in effect go to infinity at the very edge here. now, this is just a representation of what that kind of surface would be like. it's something called a hyperbolic plane. now, this remarkable sculpture done by someone named helaman ferguson, who is both a mathematician and an artist, this brings tother a lot of different aspects of infinity all in one piece. if you look at this sculpture, the cross-section is a triangle with the sides bent inward, and what's happened is that this triangle turns and twists around and then joins back up again. so it has a twist i
Search Results 0 to 1 of about 2